The general form of the considered mediation models is seen in the figure below. The set of mediators consists of some subset of saliva microbiome, plaque microbiome, and oral health outcomes (PI, ICDAS, DS, MS, FS, DT, MT, and FT). The set of outcomes consists of some subset of oral health outcomes (surfaces only) and birth outcomes (Adverse birth outcome and birth weight). Models using the salivary microbiota as mediators are based on \(n=154\) observations while those using the plaque microbiota are based on \(n=149\) observations.
General mediation model
The microbiome data were first grouped at the genus level before being transformed to relative abundance within individual and transformed with the centered log-ratio transformation to better approximate normality.
Plaque index (PI) and the international caries detection and assessment system (ICDAS) are presented on their original scale as their distributions were roughly symmetric. Each of decayed, missing, and filled surfaces (DS, MS, and FS, respectively), as true count data, were transformed with a square root before standardization so as to render their distributions more continuous and/or approximately normal. For example: \[ \text{MS}'=\frac{\sqrt{\text{MS}_i}-n^{-1}\sum_{i=1}^n \sqrt{\text{MS}_i}}{\text{sd}(\sqrt{\text{MS}})} \]
Interpretations, therefore, need to be made in terms of changes in standard deviations of the square root of the considered variable relative to the mean of the variable on the square root scale. Adverse birth outcomes is a binary variable and was thus left as-is albeit in violation of our normality assumption. Birth weight was sufficiently symmetric and was therefore left on its original scale.
The set of confounders consisted of: age, race, Hispanic (Y/N), yeast infection (Y/N), on antiobiotics (Y/N), on antifungal (Y/N), brushing twice daily (Y/N), prenatal inhaler use, prenatal diabetes status, prenatal asthma status, prenatal emotional condition, prenatal hypertension status, prenatal smoking status, employment status, modified education level (middle school/high school, Associates’ degree, or Bachelor’s degree), marriage status, number of children, cortisol level (log), estradiol level (log), progesterone level (log), testosterone level (log), T3 level (log), T4 level (log), and gestational age at first visit.
Included below are tables corresponding to each of the nine considered models. Each table contains the selected partial indirect effects (PIDEs), total indirect effect (TIDE), and direct effect (DE) of exposure (C. albicans is present). Those in the “Estimand” column that are not explicitly labeled with an effect are assumed to be the partial indirect effect from exposure to the corresponding outcome, through that mediator. Additionally, each table contains the mean and standard deviation of 5000 bootstrap samples for each of the above effects, as well as a bootstrap \(p\)-value (where the null hypothesis is an effect of 0) and two forms of bootstrap confidence intervals.
Proceeding each table is a visualization of the (partially) selected directed acyclic graph (DAG). Note that, for several of the considered models, these DAGs do not contain all selected mediators. Rather, due to limitations of interpretability, they include only those mediators that have at least one statistically significant effect. Double arrows from a mediator to an outcome represent mediation paths (i.e. \(\text{exposure}\to\text{mediator}\to\text{outcome}\)) that are statistically significant at the \(\alpha=0.05\) level based on the bootstrap inference without adjusting for multiplicity. After the DAG comes a short summary list containing all the estimated effects for each outcome. The only information contained here that is not also present in the searchable tables are the TEs, which are simply the summation of the TIDE and DE for that given outcome.
Example conclusions can be framed as follows:
Example conclusion for a (significant) PIDE: Bacterium X has a positive/negative (equiv. increasing/decreasing) mediating effect on the amount/number/value of [(sqrt)-outcome] relative to its mean [in terms of SDs]
Example conclusion for a TIDE: The selected mediation profile has an overall positive/negative (equiv. increasing/decreasing) mediating effect on the amount/number/value of [(sqrt)-outcome] relative to its mean [in terms of SDs]
Example conclusion for a (significant) DE: Ca being present has a positive/negative (equiv. increasing/decreasing) effect on the amount/number/value of [(sqrt)-outcome] relative to its mean [in terms of SDs]
Example conclusion for a TE: Ca being present, in combination with the mediation profile, has an overall positive/negative (equiv. increasing/decreasing) effect on the amount/number/value of the [(sqrt)-outcome] relative to its mean [in terms of SDs]
Model 1 DAG
The effect estimates for each outcome in model 1 are as follows:
PI: TIDE = 17.2439, DE = 0.2897, TE = 17.5336
ICDAS: TIDE = 14.2213, DE = 0.2630, TE = 14.4843
DS: TIDE = 1.8098, DE = 0.8351, TE = 2.6449
MS: TIDE = 11.5801, DE = 0.1740, TE = 11.7541
FS: TIDE = 11.7601, DE = -0.1985, TE = 11.5616
Model 2 DAG
The effect estimates for each outcome in model 2 are as follows:
PI: TIDE = 4.2059, DE = 0.4133, TE = 4.6192
ICDAS: TIDE = -14.9795, DE = 0.4842, TE = -14.4953
DS: TIDE = 10.5259, DE = 0.7025, TE = 11.2284
MS: TIDE = -17.6112, DE = 0.6277, TE = -16.9835
FS: TIDE = -13.7503, DE = 0.2881, TE = -13.4622
Model 3 DAG
The effect estimates for each outcome in model 3 are as follows:
ABO: TIDE = 0.2279, DE = 0.0274, TE = 0.2553
BW: TIDE = -1.7878, DE = 0.0209, TE = -1.7669
Model 4 DAG
The effect estimates for each outcome in model 4 are as follows:
ABO: TIDE = 2.4280, DE = 0.0270, TE = 2.4550
BW: TIDE = -6.3016, DE = 0.0588, TE = -6.2428
Model 5 DAG
The effect estimates for each outcome in model 5 are as follows:
ABO: TIDE = 0.9039, DE = 0.0038, TE = 0.9077
BW: TIDE = 4.7391, DE = -0.2509, TE = 4.4882
Model 6 DAG
The effect estimates for each outcome in model 6 are as follows:
PI: TIDE = 17.6871, DE = 0.2924, TE = 17.3947
ICDAS: TIDE = 13.3472, DE = 0.2677, TE = 13.0795
DS: TIDE = 1.8822, DE = 0.8374, TE = 1.0448
MS: TIDE = 10.6652, DE = 0.1772, TE = 10.4880
FS: TIDE = 9.3661, DE = -0.1951, TE = 9.5612
ABO: TIDE = 2.0691, DE = 0.0269, TE = 2.0422
BW: TIDE = -3.8584, DE = 0.0591, TE = -3.9175
Model 7 DAG
The effect estimates for each outcome in model 7 are as follows:
PI: TIDE = 4.7773, DE = 0.4133, TE = 4.3640
ICDAS: TIDE = -11.2637, DE = 0.4844, TE = -11.7481
DS: TIDE = 11.1998, DE = 0.7026, TE = 10.4972
MS: TIDE = -14.5112, DE = 0.6277, TE = -15.1389
FS: TIDE = -12.2207, DE = 0.2881, TE = -12.5088
ABO: TIDE = 0.2925, DE = 0.0038, TE = 0.2887
BW: TIDE = 11.1600, DE = -0.2710, TE = 11.4310
Model 8 DAG
The effect estimates for each outcome in model 8 are as follows:
PI: TIDE = 12.2156, DE = 0.3684, TE = 11.8472
ICDAS: TIDE = 5.0827, DE = 0.3083, TE = 4.7744
DS: TIDE = -2.0868, DE = 0.8411, TE = -2.9279
MS: TIDE = 11.2896, DE = 0.1686, TE = 11.1210
FS: TIDE = 2.3642, DE = -0.1917, TE = 2.5559
ABO: TIDE = 2.3014, DE = 0.0267, TE = 2.2747
BW: TIDE = -4.5914, DE = 0.0749, TE = -4.6663
Model 9 DAG
The effect estimates for each outcome in model 9 are as follows:
PI: TIDE = 11.3404, DE = 0.4461, TE = 10.8943
ICDAS: TIDE = -4.3812, DE = 0.4289, TE = -4.8101
DS: TIDE = 20.6233, DE = 0.7016, TE = 19.9217
MS: TIDE = -19.5377, DE = 0.6225, TE = -20.1602
FS: TIDE = -9.7981, DE = 0.3136, TE = -10.1117
ABO: TIDE = 0.1886, DE = 0.0039, TE = 0.1847
BW: TIDE = 8.9890, DE = -0.2720, TE = 9.2610